ON THE LINEAR THEORY OF HEAT CONDUCTION.
LEHIGH UNIV BETHLEHEM PA CENTER FOR THE APPLICATION OF MATHEMATICS
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A general linear theory of heat conduction is developed. General representation theorems are derived for the relations between energy, heat flow and temperature, temperature gradient. They contain aftereffect functions of a well defined class, the so-called positive definite functions. The results are given for isotropic as well as anisotropic materials. For a particular class of materials, noted as of the relaxation type, it is possible to give a non-equilibrium entropy in terms of a certain functional which satisfies a Clausius-Duhem inequality. Also a model for linear heat conduction in this class of materials is given which consists of a thermodynamic formalism with internal variables. Author